1. Field of the Invention
The present invention relates generally to signal processing, and more particularly, to a method and apparatus for reducing impulse noise in signals transmitted using communication services or recorded using imaging devices.
2. Description of Related Art
Currently, there is a significant desire to exploit the unused available bandwidth of the twisted pair lines of the existing plain old telephone system (POTS) for providing various digital services. Although it is believed that the future media for networked data transmission will be fiber optic based and although the main backbone of the network that interconnects the switching centers is now mainly optical fiber, the ‘last mile’ which is the access portion of the network that connects switches to customers is still dominated by twisted copper wires. For example, there exits over 560 million ‘last mile’ twisted copper pair connections globally. The estimated cost of replacing these connections with fiber optics is prohibitive and therefore the existing unused bandwidth of the POTS provides an important alternative.
Advanced digital transmission techniques such as digital subscriber line services utilize the existing unused bandwidth of the POTS for providing increased data transmission rates for available digital data transmission services. By convention, ‘digital subscriber line’ services are referred to as “DSL” services. The term “DSL” refers a connection created by a modem pair enabling high-speed digital communications. More generally, DSL is referred to as xDSL, where the ‘x’ indicates a number of different variants of the service (e.g., H (High), S (Single-Line), and A (Asymmetric)).
One factor that impairs the performance of xDSL services or other similar services that operate at high frequencies, such as integrated digital services network (ISDN), is “impulse noise.” Impulse noise is noise that occurs with high amplitudes on telephone lines or other transmission mediums. That is, samples of impulse noise have very large amplitudes that occur much more frequently than they would with Gaussian noise. Some known causes of impulse noise include electrical equipment operating near the telephone line or relay re-openings and the ringing of a telephone on the line.
In operation, xDSL services rely on modems to carry digital signals over the pass-band channels of the POTS. The modems translate digital data to analog signals at the sender end of the telephone line and translate the analog signals to digital data at the receiver end of the telephone line. The analog signal output at the receiver end of a telephone line is a corrupted version of the analog signal input at the sender end of the telephone line.
More specifically, the analog signal output from a telephone line is generally referred to as an “observed” signal. The observed signal includes a noise component and data component. An observed signal without the noise component is defined herein as a clean signal. In order to recover the data component from the observed signal, impulse noise introduced during the transmission of the data component must be identified.
One technique for recovering the data component is to estimate (i.e., predict) what the clean signal is without the noise component. Data components of output signals that are estimated are referred to herein as “cleaned” signals. One such estimation technique isolates the noise component from the data component in an observed signal by modeling the noise component using a probability density function (i.e., pdf) that describes the observed statistical properties of the noise component.
Once the noise component is accurately modeled using a pdf, the pdf can be used to define an error criterion (also referred to herein as a cost function). The error criterion is minimized to solve for model parameters, which are used to estimate the data component of a sampled signal.
A common pdf used to model noise is a Gaussian (or normal) distribution. One factor for using a Gaussian distribution to estimate noise is that the Gaussian assumption leads to simple estimation techniques. The reason the Gaussian distribution does not accurately estimate impulse noise is because impulse noise exhibits large amplitudes known as outliers that occur too frequently to fit to a Gaussian model. This characteristic suggests that the underlying probability distribution that models the noise has heavier tails as compared to a Gaussian distribution.
It has been suggested that an alpha-stable distribution is one alternative to a Gaussian distribution for modeling impulse noise. Because there exists no compact form to express its probability distribution function, an alpha-stable distribution is typically defined by its characteristic function φ(z), which is the Fourier transform of its probability density function.φ(z)=exp(jδz−γ|z|α[1+jβ sign(z)w(z,α)]}  (1) where,                α is the characteristic exponent such that 0<α≦2,        β is the symmetry parameter such that −1≦β≦1,        γ the dispersion such that γ>0,        δ is the location parameter such that −∞<δ<∞, and       w    ⁡          (              z        ,        α            )        =      {                                                      tan              ⁢                                                           ⁢                                                α                  ⁢                                                                           ⁢                  π                                2                                      ,                                                              if              ⁢                                                           ⁢              α                        ≠            1                                                                                          2                π                            ⁢                                                           ⁢              log              ⁢                                              z                                                      ,                                                              if              ⁢                                                           ⁢              α                        =            1.                                      
More specifically, the parameters control the properties of the pdf of an alpha-stable distribution as follows. The characteristic exponent α is a measure of the thickness of the tails of the alpha-stable distribution. The special case of α=2 corresponds to the Gaussian distribution, and the special case of α=1 with β=0 corresponds to the Cauchy distribution. The symmetry parameter β sets the skewness of the alpha-stable distribution. When β=0 the distribution is symmetric around the location parameter δ, in which case the alpha-stable distribution is called a symmetric alpha-stable (i.e., SαS) distribution. The location parameter δ determines the shift of the alpha-stable distribution from the origin, and is the mean (if 1<α≦2) or median (if β=0) of the alpha-stable distribution. Finally, the dispersion γ measures the deviation around the mean in a manner similar to the variance of a Gaussian distribution.
Alpha-stable distributions have been used to design systems for detecting signals in the presence of impulse noise. (See for example, E. E. Kuruoglu, W. J. Fitzgerald and P. J. W. Rayner, “Near Optimal Detection of Signals in Impulsive Noise Modeled with a Symmetric alpha-Stable Distribution”, IEEE Communications Letters, Vol. 2, No. 10, pp. 282-284, October 1998.) However, most of these systems that use alpha-stable distributions in their statistical models, assume a priori knowledge of the parameters of the alpha-stable distribution. Systems that assume a priori knowledge of the parameters of an alpha-stable distribution pre-assign values for the parameters. Having the ability to estimate, and not pre-assign, the value of parameters of the alpha-stable distribution is vital since most existing systems are sensitive to the parameters of the alpha-stable distribution that models the impulse noise.
Existing methods for estimating parameters of an alpha-stable distribution generally provide limited solutions for the special case of a symmetric alpha-stable distribution (SαS) (i.e., where the parameter β=0). Assuming that an alpha-stable distribution is symmetric, however, may yield a poor model of impulse noise because impulse noise tends to be more accurately modeled by skewed rather than symmetric distributions. Existing methods for estimating the parameters of an alpha-stable distribution, which provide general solutions that are not limited to the special case of a symmetric distribution, tend to be computationally expensive or provide estimates with high variances.
It would be advantageous therefore to provide an improved system for modeling additive impulse noise corrupting data streams. Furthermore, it would be advantageous if such a system were able to model impulse noise using an alpha-stable distribution. Also, it would be advantageous if the improved system were able to adaptively estimate, and not pre-assign, the parameters of an alpha-stable distribution.